Correlation Matrix Heat-map

Below shows a correlation heat-map of the submitted variables.

Regression Analysis

Model formulation

The following outlines the regression formula and summary of the model fitted.


## [1] "freq ~ rank"
  Dependent variable
Predictors Estimates std. Error CI Statistic p
(Intercept) 7.30 0.07 7.16 – 7.44 104.51 <0.001
rank -0.07 0.00 -0.08 – -0.07 -57.89 <0.001
Observations 5644
R2 / R2 adjusted 0.373 / 0.373
AIC 30754.242


Residual Plots

The residual plots for the fitted regression model are shown below.




Statistical Tests

The ANOVA test is used to determine if there is a statistically significant difference between the means of three or more independent groups. ANOVA test results for the fitted model are shown below.

## ANOVA Table (type II tests)
## 
##   Effect DFn  DFd        F p p<.05   ges
## 1   rank   1 5642 3351.501 0     * 0.373



A t-test is a statistical test used to determine if their is a significant difference in the means of two independent groups being compared. The results of the t-test for the fitted model are shown below.